<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>









<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:50_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 ;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E2:50_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:50_1"/><b>then </b><i><font color="Green">E34</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>thus </b><i><font color="Green">E35</font></i>: the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> = 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self">Def2</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="fsm_1.html#E3:50_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="fsm_1.html#E1:50_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:50_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self">Def2</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:50_1_2"/>
( <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:50_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="fsm_1.html#D10" target="_self">Def10</a>, <a class="ref" href="fsm_1.html#T35" target="_self">Th35</a></i>;<br/><b>hence </b><a NAME="E2:50_1_2"/>
<span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:50_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:50_1"/>
the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:50"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <br/>( the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K1">]</a></span> &amp; the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a>  )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D10" target="_self">FSM_1:def 10</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:50_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1"><b>suppose </b></a><a NAME="E1:50_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  = 
 <a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="fsm_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:50_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fsm_1.html#T24" target="_self">Th24</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_2"><b>suppose </b></a><a NAME="E1:50_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:50_2_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T111">FINSEQ_3:111</a></i>;<br/><b>set </b><font color="Maroon">c<sub>10</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><a NAME="E4:50_2_2"/>
the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:50"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E5:50_2_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/><b>set </b><font color="Maroon">c<sub>12</sub></font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  = 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:50_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fsm_1.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:50"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fsm_1.html#E5:50_2_2"><i><font color="Green">E35</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:50_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="fsm_1.html#T35" target="_self">Th35</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
